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Sobre funciones de negación en la teoría de conjuntos difusos.

Enric Trillas (1979)

Stochastica

En su trabajo de 1973, ya clásico, Bellman y Giertz probaron que P(X) es un retículo distributivo con máximo y mínimo sólo (con hipótesis muy razonables) bajo las usuales definiciones (A U B)(x) = máx {A(x),B(x)}, (A ∩ B)(x) = mín {A(x),B(x)}, tratando escasamente el formalismo analítico relativo a la negación. En el presente trabajo se prueba que tal P(X) es un álgebra de DeMorgan si y sólo si la función de negación posee generador aditivo y que tales negaciones constituyen, en un cierto grupo...

Software cost estimation with fuzzy inputs: Fuzzy modelling and aggregation of cost drivers

Miguel-Ángel Sicilia, Juan-J. Cuadrado-Gallego, Javier Crespo, Elena García Barriocanal (2005)

Kybernetika

Parametric software cost estimation models are well-known and widely used estimation tools, and several fuzzy extensions have been proposed to introduce a explicit handling of imprecision and uncertainty as part of them. Nonetheless, such extensions do not consider two basic facts that affect the inputs of software cost parametric models: cost drivers are often expressed through vague linguistic categories, and in many cases cost drivers are better expressed in terms of aggregations of second-level...

Some methods to obtain t-norms and t-conorms on bounded lattices

Gül Deniz Çaylı (2019)

Kybernetika

In this study, we introduce new methods for constructing t-norms and t-conorms on a bounded lattice L based on a priori given t-norm acting on [ a , 1 ] and t-conorm acting on [ 0 , a ] for an arbitrary element a ∈ L ∖ { 0 , 1 } . We provide an illustrative example to show that our construction methods differ from the known approaches and investigate the relationship between them. Furthermore, these methods are generalized by iteration to an ordinal sum construction for t-norms and t-conorms on a bounded lattice.

Some notes on the category of fuzzy implications on bounded lattices

Amin Yousefi, Mashaallah Mashinchi, Radko Mesiar (2021)

Kybernetika

In this paper, we introduce the product, coproduct, equalizer and coequalizer notions on the category of fuzzy implications on a bounded lattice that results in the existence of the limit, pullback, colimit and pushout. Also isomorphism, monic and epic are introduced in this category. Then a subcategory of this category, called the skeleton, is studied. Where none of any two fuzzy implications are Φ -conjugate.

Some notes on U-partial order

M. Nesibe Kesicioğlu, Ü. Ertuğrul, F. Karaçal (2019)

Kybernetika

In this paper, an equivalence on the class of uninorms on a bounded lattice is discussed. Some relationships between the equivalence classes of uninorms and the equivalence classes of their underlying t-norms and t-conorms are presented. Also, a characterization for the sets admitting some incomparability w.r.t. the U-partial order is given.

Some properties of residuated lattices

Radim Bělohlávek (2003)

Czechoslovak Mathematical Journal

We investigate some (universal algebraic) properties of residuated lattices—algebras which play the role of structures of truth values of various systems of fuzzy logic.

Some results on the weak dominance relation between ordered weighted averaging operators and T-norms

Gang Li, Zhenbo Li, Jing Wang (2024)

Kybernetika

Aggregation operators have the important application in any fields where the fusion of information is processed. The dominance relation between two aggregation operators is linked to the fusion of fuzzy relations, indistinguishability operators and so on. In this paper, we deal with the weak dominance relation between two aggregation operators which is closely related with the dominance relation. Weak domination of isomorphic aggregation operators and ordinal sum of conjunctors is presented. More...

Specifying t-norms based on the value of T (1/2, 1/2).

Marcin Detyniecki, Ronald R. Yager, Bernadette Bouchon-Meunier (2000)

Mathware and Soft Computing

We study here the behavior of the t-norms at the point (1/2, 1/2). We indicate why this point can be considered as significant in the specification of t-norms. Then, we suggest that the image of this point can be used to classify the t-norms. We consider some usual examples. We also study the case of parameterized t-norms. Finally using the results of this study, we propose a uniform method of computing the parameters. This method allows not only having the same parameter-scale for all the families,...

Sufficient conditions for a T-partial order obtained from triangular norms to be a lattice

Lifeng Li, Jianke Zhang, Chang Zhou (2019)

Kybernetika

For a t-norm T on a bounded lattice ( L , ≤ ) , a partial order ≤ T was recently defined and studied. In [11], it was pointed out that the binary relation ≤ T is a partial order on L , but ( L , ≤ T ) may not be a lattice in general. In this paper, several sufficient conditions under which ( L , ≤ T ) is a lattice are given, as an answer to an open problem posed by the authors of [11]. Furthermore, some examples of t-norms on L such that ( L , ≤ T ) is a lattice are presented.

Sum of observables in fuzzy quantum spaces

Anatolij Dvurečenskij, Anna Tirpáková (1992)

Applications of Mathematics

We introduce the sum of observables in fuzzy quantum spaces which generalize the Kolmogorov probability space using the ideas of fuzzy set theory.

Symmetric implicational restriction method of fuzzy inference

Yiming Tang, Wenbin Wu, Youcheng Zhang, Witold Pedrycz, Fuji Ren, Jun Liu (2021)

Kybernetika

The symmetric implicational method is revealed from a different perspective based upon the restriction theory, which results in a novel fuzzy inference scheme called the symmetric implicational restriction method. Initially, the SIR-principles are put forward, which constitute optimized versions of the triple I restriction inference mechanism. Next, the existential requirements of basic solutions are given. The supremum (or infimum) of its basic solutions is achieved from some properties of fuzzy...

(T, ⊥, N) fuzzy logic.

Y. Xu, J. Lin, Da Ruan (2001)

Mathware and Soft Computing

To investigate more reasonable fuzzy reasoning model in expert systems as well as more effective logical circuit in fuzzy control, a (T, ⊥, N) fuzzy logic is proposed in this paper by using T-norm, ⊥-norm and pseudo-complement N as the logical connectives. Two aspects are discussed: (1) some concepts of (T, ⊥, N) fuzzy logic are introduced and some properties of (T, ⊥, N) fuzzy logical formulae are discussed. (2) G-fuzzy truth (falsity) of (T, ⊥, N) fuzzy logical formulae are investigated and also...

The prime and maximal spectra and the reticulation of BL-algebras

Laurenťiu Leuštean (2003)

Open Mathematics

In this paper we study the prime and maximal spectra of a BL-algebra, proving that the prime spectrum is a compact T 0 topological space and that the maximal spectrum is a compact Hausdorff topological space. We also define and study the reticulation of a BL-algebra.

The study on semicopula based implications

Zuming Peng (2020)

Kybernetika

Recently, Baczyński et al. (2017) proposed a new family of implication operators called semicopula based implications, which combines a given a priori fuzzy implication and a semicopula. In this paper, firstly, the relationship between the basic properties of the priori fuzzy implication and the semicopula based implication are analyzed. Secondly, the conditions such that the semicopula based implication is a fuzzy implication are studied, the study is carried out mainly in the case that the semicopula...

Towards an extension of the 2-tuple linguistic model to deal with unbalanced linguistic term sets

Mohammed-Amine Abchir, Isis Truck (2013)

Kybernetika

In the domain of Computing with words (CW), fuzzy linguistic approaches are known to be relevant in many decision-making problems. Indeed, they allow us to model the human reasoning in replacing words, assessments, preferences, choices, wishes... by ad hoc variables, such as fuzzy sets or more sophisticated variables. This paper focuses on a particular model: Herrera and Martínez' 2-tuple linguistic model and their approach to deal with unbalanced linguistic term sets. It is interesting since the...

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